It is already known that N-aryl-trifluoroacetoacet-amides can be prepared by reacting trifluoroacetoacetic ester with aryl amines (cf. DE-A 42 18 159, EP-A 0 598 436 and J. Het. Chem. 2 (1965), 124). However, this process has the disadvantages that it is not widely applicable and that the desired products are only obtained in relatively low yields owing to interfering side reactions. Thus, to a considerable extent, the aryl amine attacks the carbonyl group which is adjacent to the trifluoromethyl group. The resulting enamine readily reacts with a further arylamine molecule, giving bis-adducts. This reaction can be illustrated by the following equation: ##STR3## Furthermore, it is known that N-aryl-trifluoroacetoacet-amides can be prepared by eliminating one molecule of aryl amine from the bis-adducts of the abovementioned structure (cf. DE-A 42 18 159). It is a disadvantage of this process that it requires one step more than the method described above. Moreover, even here the yields are unsatisfactory for realizing the reaction on an industrial scale.